TY - JOUR
T1 - Analysis of average run length for CUSUM procedure with negative exponential data
AU - Busaba, Jaruchat
AU - Sukparungsee, Saowanit
AU - Areepong, Yupaporn
AU - Mititelu, Gabriel
PY - 2012
Y1 - 2012
N2 - The Average Run Length (ARL) is a performance measure that is frequently used in control charts. Cumulative Sum (CUSUM) is a popular procedure in quality control as it is a sensitive detector of small shifts in values of distribution parameters. In this paper, we use an integral equation approach to derive explicit formulas for the ARL (the first passage times) for CUSUM when observations are negative exponential distributed. Simulations are carried out to compare the performance of the explicit formulas with that of numerical approximations. The computational time for the explicit formulas is found to be approximately 10 seconds, which is much less than the computational time required for numerical approximations.
AB - The Average Run Length (ARL) is a performance measure that is frequently used in control charts. Cumulative Sum (CUSUM) is a popular procedure in quality control as it is a sensitive detector of small shifts in values of distribution parameters. In this paper, we use an integral equation approach to derive explicit formulas for the ARL (the first passage times) for CUSUM when observations are negative exponential distributed. Simulations are carried out to compare the performance of the explicit formulas with that of numerical approximations. The computational time for the explicit formulas is found to be approximately 10 seconds, which is much less than the computational time required for numerical approximations.
KW - CUSUM technique
KW - integral equations
KW - numerical integration
UR - https://hdl.handle.net/1959.7/uws:57778
UR - https://epg.science.cmu.ac.th/ejournal/journalDetail.php?journal_id=1042
M3 - Article
SN - 0125-2526
VL - 39
SP - 200
EP - 208
JO - Chiang Mai Journal of Science
JF - Chiang Mai Journal of Science
IS - 2
ER -